A SPARSE-GRID METHOD FOR MULTI-DIMENSIONAL BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS

作     者：Guannan Zhang Max Gunzburger Weidong Zhao 

作者机构：Department of Scientific Computing Florida State University Tallahassee FL 32306Computer Science and Mathematics Division Oak Ridge National Lab Oak Ridge TN 37831 Department of Scientific Computing Florida State University Tallahassee FL 32306 School of Mathematics Shandong University Jinan Shandong 250100 China 

出 版 物：《Journal of Computational Mathematics》 (计算数学（英文）)

年 卷 期：2013年第31卷第3期

页      面：221-248页

核心收录：

学科分类：02[经济学] 0202[经济学-应用经济学] 020208[经济学-统计学] 07[理学] 08[工学] 0714[理学-统计学（可授理学、经济学学位）] 070103[理学-概率论与数理统计] 0701[理学-数学] 080102[工学-固体力学] 0801[工学-力学（可授工学、理学学位）] 

基　　金：Acknowledgments. The first author was supported by the US Air Force Office of Scientific Research under grant FA9550-11-1-0149. The first author was also supported by the Advanced Simulation Computing Research (ASCR)  Department of Energy  through the Householder Fellowship at ORNL. The ORNL is operated by UT-Battelle  LLC  for the United States Depart-ment of Energy under Contract DE-AC05-00OR22725. The second author was supported by the US Air Force Office of Scientific Research under grant FA9550-11-1-0149. The third author was supported by the Natural Science Foundation of China under grant 11171189. The third author was also supported by the Natural Science Foundation of China under grant 91130003. The thrid author was also supported by Shandong Province Natural Science Foundation under grant ZR2001AZ002 

主　　题：Backward stochastic differential equations Multi-step scheme Gauss-Hermite quadrature rule Adaptive hierarchical basis Sparse grids. 

摘      要：A sparse-grid method for solving multi-dimensional backward stochastic differential equations （BSDEs） based on a multi-step time discretization scheme [31] is presented. In the multi-dimensional spatial domain, i.e. the Brownian space, the conditional mathe- matical expectations derived from the original equation are approximated using sparse-grid Gauss-Hermite quadrature rule and （adaptive） hierarchical sparse-grid interpolation. Error estimates are proved for the proposed fully-discrete scheme for multi-dimensional BSDEs with certain types of simplified generator functions. Finally, several numerical examples are provided to illustrate the accuracy and efficiency of our scheme.